The present invention relates to electrical resistivity logging of wellbores. More specifically, the present invention relates to logging operations to determine the electrical resistivity of earth formations from within a metallic wellbore casing.
Electrical resistivity measurements of earth formations indicate the presence of oil and gas in the earth formations. Numerous devices are known in the art for measuring earth formation resistivity. Known devices such as sondes and other logging tools for measuring resistivity are typically lowered by one end of an armored electrical cable into the wellbore. Equipment at the wellbore surface is electrically connected to the other end of the cable, and electrical signals corresponding to formation resistivity are transmitted from the logging tool to surface equipment.
Logging tools originally required an xe2x80x9copen holexe2x80x9d wellbore that does not have a steel pipe such as tubing or casing in the wellbore. Casing is inserted into wellbores to maintain the mechanical and hydraulic integrity of the wellbore. However, formation resistivity logging tools are adversely affected by the presence of wellbore casing since the casing resistivity can be smaller than 10xe2x88x927 to 10xe2x88x9210 times the earth formation resistivity. The large resistivity contrast between casing and formation inhibits measurements made by the typical resistivity measuring devices.
Many efforts have been proposed to determine formation resistivity through a casing. A representative system for measuring resistivity in a cased wellbore was described in U.S. Pat. No. 5,075,626 issued to Vail (1991). A logging sonde having multiple electrodes was lowered by one end of an armored cable into the wellbore so that sonde electrodes were activated to make electrical contact with the casing. An electric current source was connected to one of the tool electrodes and to a current return electrode at the wellbore surface. The source comprised a low-frequency alternating current source having a frequency less than 10 Hz. Electrical current was injected into the casing and traveled both upwardly and downwardly through the casing. Current xe2x80x9cleaksxe2x80x9d outwardly into the earth formations decreased the voltage measured along the casing as a function of the distance from the electrode. By measuring the current leakage (⊕I) within a particular interval, the resistivity of the earth formation contacting the casing could be determined. If Vo represents the voltage on the casing with respect to infinity, then the resistivity of the formation near the wellbore within the axial boundaries of the measured interval is calculable by the expression: Vo xcex94I. Apparent resistivity within the interval was defined by the expression:                               ρ          a                =                              k            ·            Δ                    ⁢                      xe2x80x83                    ⁢                      z            ·                                          V                o                                            Δ                ⁢                                  xe2x80x83                                ⁢                I                                                                        (        1        )            
wherein k is a dimensionless constant providing equality of apparent resistivity to the formation resistivity, assuming that the casing and formation are each homogeneous, and xcex94Z represents the interval length along the casing.
To determine resistivity of the formation through the casing, the characteristic impedance (Q) was determined by energizing an emitter electrode and by connecting the other terminal to a surface electrode. In addition to voltage drops measured by first, second and third voltage measuring circuits, voltage drop was measured by a fourth voltage measuring circuit between a surface potential electrode and a voltage sensing electrode within the sonde. The characteristic impedance was calculated from the voltage Vo measured by a fourth measuring circuit according to the formula:                     Q        =                              V            o                                I            o                                              (        2        )            
wherein Io represents the amount of current imparted by the source. The resistance of the particular casing section located between electrode pairs was determined, and the current from the source was returned to a current return electrode on the sonde rather than to the surface electrode. Substantially all of the electrical current flowed along the casing between the emitter electrode and the current return electrode on the sonde. The current flow in such electrical configuration is referred to by In, and the current amount leaking from the casing in such electrical configuration is negligible.
The first voltage measuring circuit measured a voltage drop, represented by Vxe2x80x21, between an electrode pair for detecting the casing resistance between the electrodes. Similarly, the second voltage measuring circuit measured a voltage drop, Vxe2x80x22, between another electrode pair. The resistances of the casing between such electrode pair, were determined by the expression:                                           R            1                    =                                    V              1              xe2x80x2                                      I              n                                      ;                  xe2x80x83                ⁢                              R            2                    =                                    V              2              xe2x80x2                                      I              n                                                          (        3        )            
A third voltage measuring circuit determined a second difference referred to as xcex94V between voltage measurements made by the first and second measuring circuits. The current source was then reconnected to return the current at the surface electrode, and the current flow from the source in such electrical configuration was referred to as Im. Voltage drop V1 was again measured by the first measuring circuit between a first electrode pair. Voltage drop V2 was also again measured by the second measuring circuit between the second electrode pair. Another second difference, referred to as xcex94Vxe2x80x2, was also measured by the third measuring circuit. The average current flowing along the casing between the first electrode pair was related to V1/R1, and the average current flowing along the casing between the second electrode pair was related to V2/R2. The average current flowing between the first electrode pair was slightly different from the average current flowing between the second electrode pair because of current leaks out of the casing into the formation. The amount of leakage current, xcex94I, was determined according to the expression:                               Δ          ⁢                      xe2x80x83                    ⁢          I                =                                            V              1                                      R              1                                -                                    V              2                                      R              2                                                          (        4        )            
The voltage present on the casing, with respect to infinity, was determined as Qxc2x7Im. By substitution of Equations (3) and (4) into equation (1), the apparent resistivity of the formation was determined by the expression:                               ρ          a                =                  K          ·          Q          ·                                    I              m                                      I              n                                ·                                    [                                                                    V                    1                                                        V                    1                    xe2x80x2                                                  -                                                      V                    2                                                        V                    2                    xe2x80x2                                                              ]                                      -              1                                                          (        5        )            
where K is a constant of proportionality, called a xe2x80x9ctool factorxe2x80x9d, related by the expression:
K=kxc2x7xcex94zxe2x80x83xe2x80x83(6)
xcex94z is equal to the spacing between the first electrode pair.
The difference of the current flow between the first electrode pair and the current flow between second electrode pair is very small as previously explained. Substitution of the second difference measurements into Equation 5 results in the following expressions for apparent resistivity of the formation 6:                               ρ          a                =                  K          ·          Q          ·          A          ·                                    [                                                                    Δ                    ⁢                                          xe2x80x83                                        ⁢                    V                                                        V                    1                                                  -                                                                            "AutoLeftMatch"                                              Δ                        ⁢                                                  xe2x80x83                                                ⁢                        V                                            "AutoRightMatch"                                        xe2x80x2                                                        V                    1                    xe2x80x2                                                              ]                                      -              1                                                          (        7        )            
where A in Equation (7) is equal to:                     A        =                                                            V                1                xe2x80x2                            /                              I                n                                                                    V                1                            /                              I                m                                              ⁡                      [                          1              -                                                                    "AutoLeftMatch"                                          Δ                      ⁢                                              xe2x80x83                                            ⁢                      V                                        "AutoRightMatch"                                    xe2x80x2                                                  V                  1                  xe2x80x2                                                      ]                                              (        8        )            
As described by U.S. Pat. No. 5,075,626 the combination of these three electrical configurations provide information to determine resistivity of the formation measured from inside a conductive casing. However, this approach is significantly limited because the three measurements are performed sequentially. Due to the very small signals and low frequency, up to several minutes measurement time can be required per measurement. The measurements require two separate surface electrodes to be installed several hundred feet away from the well head, and require at least three sequential, extremely accurate measurements. The cumulative time necessary to survey each wellbore section disrupts other operations and limits overall well productivity.
Other systems have been developed for determining formation resistivity through casing. In U.S. Pat. No. 4,837,518 to Gard et al. (1989), a low frequency bipolar voltage was applied to casing and a switching network alternately connects differential outputs. In U.S. Pat. No. 5,223,794 to Vail (1993), resistance between two electrode pairs was determined, and first and second error information was determined to evaluate formation resistivity. In U.S. Pat. No. 5,510,712 to Sezginer et al. (1996), voltages were measured between a first casing part and an intermediate section, and between a second casing part and the intermediate section. In U.S. Pat. No. 5,809,458 to Tamarchenko (1996), a model of earth formations and casing was initialized and the conductance of individual segments was calculated. In U.S. Pat. No. 5,563,514 to Moulin (1996), a wheatstone bridge was balanced across circuits detecting the resistance across two casing sections. In U.S. Pat. No. 5,543,715 to Singer et al. (1996), formation resistivity was determined by combining first through fifth voltages, current measurements, and second voltage differences. In U.S. Pat. No. 5,633,590 to Vail (1997), formation resistivity measurements through wellbore casing were combined with porosity measurements to evaluate the quantity of hydrocarbons relative to formation water.
The accuracy and speed of formation resistivity measurements is important to the efficient evaluation of subsurface hydrocarbon formations. Accordingly, a need exists for an improved system for measuring formation resistivity through wellbore casing. The system should be reliable and should limit disruption to other wellbore operations.
The invention provides an apparatus and method for measuring geologic formation resistivity through a wellbore casing. The apparatus comprises a housing moveable through the casing, first and second current electrodes attached to the housing for contacting the casing, at least three electrodes attached to the housing between the first and second current electrodes for contacting the casing, wherein two of said electrodes are correlated to form at least two electrode pairs corresponding to a different, non-overlapping axial interval along the casing, at least two voltage measuring circuits each connected with one of the electrode pairs, a voltage difference measuring circuit interconnected between two of the voltage measuring circuits, wherein the voltage difference measuring circuit is capable of measuring a second difference in voltage between the voltage measuring circuits, a surface return electrode engaged with the geologic formation, a first source of electrical current connected between the first current electrode and the surface return electrode, a second source of electrical current connected between the second current electrode and the surface return electrode, and current measuring circuits for detecting current output of the first and second sources.
The method of the invention comprises the steps of measuring the electrical resistance of conductors within a cable, attaching the cable conductors to first and second electrical current sources, to a surface return electrode, to first and second current electrodes attached to a housing, and to at least three detector electrodes located at axially spaced apart locations along the housing, lowering the cable and attached housing to a selected location within the wellbore, operating the first electrical source to apply a first electrical current between the first current electrode and the surface return electrode, operating the second electrical source to apply a second electrical current between the second current electrode and the surface return electrode, measuring a first current in amplitude and phase flowing to a first current electrode, measuring a second current in amplitude and phase flowing to a second current electrode, measuring a first voltage in amplitude and phase between a first pair of the first and second detector electrodes, measuring a second voltage in amplitude and phase between a second pair of the second and third detector electrodes, measuring the difference in amplitude and phase between the first and second voltages, and determining the earth formation resistivity from the measurements of the conductors"" cable resistance, the first current, the second current, the first voltage, the second voltage, and the second difference of the voltages.